11. Interfacial Mechanism and Kinetics of Phase-Transfer Catalysis

According to Eqs. (57)–(61), and for organic volume V and interfacial area S, the rate ofchange of solute concentration can be expressed byV d½QXŠ¼ KS dt o m½QXŠ m½QXŠ ð62Þin whichK o ¼ m þ 1 þ m 1ð63Þk a k m k oAccording to the initial extractive concept that the content of quaternary salt is restrictedto less than 10% in the aqueous solution, the quaternary salt is completely dissociated, i.e.,[QX] approaches zero, and the magnitude of the distribution coefficient m is less than 10.By plotting ðV=SÞd½QXŠ=dt against ½QX], the overall mass transfer coefficient K o wasobtained by a least-squares regression. The regression factor is more than 0.99.If the extraction system is conducted in the absence of membrane, Eq. (63) is rewrittenasK o ¼m þ 1 1ð64Þk a k oThe values of diffusivities predicted for quaternary salts in the aqueous phase andthe organic phase are in the following descending order: TBPB > TBAB > TBAI BTBAB and RBAB > TBAI > TBPB > BTBAB; respectively. The diffusivities of quaternarysalts increased with increasing temperature. The effects of solvents on diffusivitiesare ranked in the following descending order: CH 2 Cl 2 > C 6 H 5 CH 3 > CHCl 3 > C 6 H 6 >C 6 H 5 Cl > 1; 2-C 2 H 4 Cl 2 > H 2 O. The main influencing factor may be the viscosity of solvent.The overall mass transfer coefficients were determined by Lin [127]. The values of k o ,k a ,andk m were calculated by a numerical method for four types of quaternary salts inseven kinds of solvents. Assuming that the hydrodynamic characteristics of the diffusionboundary layer in the aqueous phase and the organic phase were similar in the presence orabsence of the membrane system if the agitation rate was kept below 100 rpm, the individualmass transfer coefficient of the membrane could then be calculated by subtractingEq. (64) from Eq. (63). The individual mass transfer coefficients increased with increasingagitation rates and temperatures. The sequence of mass transfer coefficient isk a k o > k m .Kiani et al. [125] and Prasad et al. [126] reported the following equation for theintrinsic mass transfer coefficient in the membrane, k m ¼ D"= m , where " and m are theporosity and thickness of the membrane, respectively, is the tortuosity factor of themembrane defined as the actual pore length divided by the membrane thickness, and Dis the diffusivity of species in the bulk liquid phase. The average tortuosities were calculatedand found to reduce from 4.3 to 2.7 when the agitation rates increased from 90 to 600rpm. Because the individual mass transfer coefficient of a membrane is not a constant andincreases with increasing agitation rate, the tortuosity decreases slightly with increasingagitation rate according to the equation of Kinai et al. [125].If the mixing is so vigorous that the diffusion boundary layer can be eliminated, Eq.(62) can be reduced toVSd½QXŠdt k m m½QXŠ m½QXŠka ;k o !1¼ ð65ÞCopyright © 2003 by Taylor & Francis Group, LLC